Question

use the information given in the diagram of △ghi to find the missing measurements. round all answers to the nearest tenth. m∠g = hi = gh = 39° 30

Explanation:

Step1: Find angle G

Sum of angles in a triangle is 180°. So $m\angle G=180 - 90 - 39=51^{\circ}$

Step2: Find HI

Using $\sin39^{\circ}=\frac{HI}{30}$, then $HI = 30\times\sin39^{\circ}\approx18.9$

Step3: Find GH

Using $\cos39^{\circ}=\frac{GH}{30}$, then $GH = 30\times\cos39^{\circ}\approx23.4$

Answer:

$m\angle G = 51^{\circ}$, $HI\approx18.9$, $GH\approx23.4$